Quantum Corrections as a Bound for Detecting Self-Interacting Ultralight Dark Matter

We investigate the implications of interactions between ultralight dark matter (ULDM) and Standard Model fermions for the radiative stability of the ULDM potential. By matching the heavy fermion onto a low-energy scalar effective field theory, we derive the one-loop threshold corrections to the ULDM mass and self-interaction couplings. We interpret these corrections in terms of radiative naturalness conditions defined within the threshold-matching prescription adopted here. For the parameter region motivated by cosmological and galactic considerations, the quadratic correction provides the strongest naturalness criterion. The precise numerical contour associated with this criterion is prescription-dependent. Nevertheless, the calculation exhibits the generic sensitivity of an unprotected ultralight scalar mass to the heavy-fermion scale. For the benchmark boundary condition aR(mf)=0 and for Yukawa couplings satisfying the scalar-mass naturalness criterion, both the direct and cubic-induced quartic corrections remain subdominant relative to the cosmologically required quartic coupling.